# std::tanh(std::valarray)

From cppreference.com
< cpp‎ | numeric‎ | valarray

Defined in header `<valarray>` |  |
template< class T > valarray<T> tanh( const valarray<T>& va ); |  |

For each element in va computes hyperbolic tangent of the value of the element.

### Parameters

va | - | value array to apply the operation to

### Return value

Value array containing hyperbolic tangent of the values in va.

### Notes

Unqualified function (tanh) is used to perform the computation. If such function is not available, std::tanh is used due to argument-dependent lookup.

The function can be implemented with the return type different from std::valarray. In this case, the replacement type has the following properties:

  - All const member functions of std::valarray are provided.
  - std::valarray, std::slice_array, std::gslice_array, std::mask_array and std::indirect_array can be constructed from the replacement type.
  - For every function taking a const std::valarray<T>& except `begin()` and `end()`(since C++11), identical functions taking the replacement types shall be added;
  - For every function taking two const std::valarray<T>& arguments, identical functions taking every combination of const std::valarray<T>& and replacement types shall be added.
  - The return type does not add more than two levels of template nesting over the most deeply-nested argument type.

### Possible implementation

    template<class T>
    valarray<T> tanh(const valarray<T>& va)
    {
        valarray<T> other = va;
        for (T& i : other)
            i = tanh(i);

        return other; // proxy object may be returned
    }

### Example

Run this code

    #include <cmath>
    #include <iostream>
    #include <valarray>

    auto show = [](char const* title, const std::valarray<double>& va)
    {
        std::cout << title << " :";
        for (auto x : va)
            std::cout << "  " << std::fixed << x;
        std::cout << '\n';
    };

    int main()
    {
        const std::valarray<double> x = {.0, .1, .2, .3};
        const std::valarray<double> sinh = std::sinh(x);
        const std::valarray<double> cosh = std::cosh(x);
        const std::valarray<double> tanh = std::tanh(x);
        const std::valarray<double> tanh_by_def = sinh / cosh;
        const std::valarray<double> tanh_2x = std::tanh(2.0 * x);
        const std::valarray<double> tanh_2x_by_def =
            (2.0 * tanh) / (1.0 + std::pow(tanh, 2.0));

        show("x              ", x);
        show("tanh(x)        ", tanh);
        show("tanh(x) (def)  ", tanh_by_def);
        show("tanh(2*x)      ", tanh_2x);
        show("tanh(2*x) (def)", tanh_2x_by_def);
    }

Output:

    x               :  0.000000  0.100000  0.200000  0.300000
    tanh(x)         :  0.000000  0.099668  0.197375  0.291313
    tanh(x) (def)   :  0.000000  0.099668  0.197375  0.291313
    tanh(2*x)       :  0.000000  0.197375  0.379949  0.537050
    tanh(2*x) (def) :  0.000000  0.197375  0.379949  0.537050

### See also

sinh(std::valarray) | applies the function std::sinh to each element of valarray (function template)
cosh(std::valarray) | applies the function std::cosh to each element of valarray (function template)
tanhtanhftanhl (C++11)(C++11) | computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x)) (function)
tanh(std::complex) | computes hyperbolic tangent of a complex number (\({\small\tanh{z}}\)tanh(z)) (function template)

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